RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 26 - Linear Programming Problems>EXERCISE>Q 2

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An LPP must have a finite number of optimal solutions.

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Important Questions on Linear Programming Problems

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IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 26 - Linear Programming Problems>EXERCISE>Q 2

The feasible region of an LPP with two decision variable is bounded if it can be confined within a circle.

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RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 26 - Linear Programming Problems>EXERCISE>Q 2

If

a x + b y \leq c

be a constraint of an LPP, then an edge of its feasible region must lie on the line

a x + b y = c

.

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RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 26 - Linear Programming Problems>EXERCISE>Q 2

An LPP of which two constraints are

3 x - 5 y \geq 7

and

10 y \geq 9 + 6 x

has no optimal solution.

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RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 26 - Linear Programming Problems>EXERCISE>Q 2

The set

\{(x, y) \in R \times R : 2 x + 3 y = 7\}

is not a convex set in two dimension.

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RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 26 - Linear Programming Problems>EXERCISE>Q 2

The set

\{(x, y) \in R \times R : y^{2} \leq 4\}

is a convex set in two dimension.

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RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 26 - Linear Programming Problems>EXERCISE>Q 2

If each of the infinitely many optimal solutions of an LPP with objective function

z = a x + b y

, lies on the line

15 x + 25 y = 32

then

5 a = 3 b

.

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RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 26 - Linear Programming Problems>EXERCISE>Q 3

Consider an LPP given by Max $z = 3 x + 2 y$ subject to $x - 4 y \leq 4$ , $5 x + 4 y \leq 20$ , $y \leq 6$ where, $x \geq 0, y \geq 0$ . What are the redundant constraints of this LPP.

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RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 26 - Linear Programming Problems>EXERCISE>Q 3

Find optimal solution of the following LPP,

Maximize $z = 2 x + 3 y$ subject to $5 x + 4 y \leq 20$ , where $x \geq 0, y \geq 0$ .